5 th Grade Math Curriculum Map

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1 5.N., 5.N., 5.N.3, 5.N., Reading and writing large numbers. Representing large numbers using number lines. Using estimation to place numbers on a number line. Developing number sense for large numbers. Comparing and ordering large numbers. Rounding large numbers Unit : Big Numbers Lesson : Reading and Writing Big Numbers Billion Digit Expanded form Million Period Place Place Value Chart Rounding Standard Form Value Word Form 5.N. Self-assessing the multiplication and division facts. Maintaining fluency with the multiplication and division facts. Unit : Big Numbers Lesson: Facts I Know Divisor Fact Families Factors Product Quotient Turn-around facts Multiplication Facts I Know Division Facts I Know URG pg. 5 & 53 5.N.3, 5.N.37 Understanding place value. Representing large numbers with base-ten pieces. Translating between different representations of large numbers (concrete, pictorial, symbolic) Modeling addition and subtraction with base ten pieces. Estimating with base tem pieces. Developing number sense for large numbers Unit : Big Numbers Lesson 3: The Base-Ten Number System Base-Ten Pieces Bits Fewest Pieces rule Flats Packs Place Value Skinnies Page of 7 Rondout Valley Central School District Last Updated August 3, 005

2 5.N., 5.N., 5.N.6, 5.N., 5.N7 Multiplying numbers ending with zero. Modeling multiplication with base-ten pieces. Understanding paper and pencil methods for multiplication. Multiplying using paper and pencil methods Unit : Big Numbers Lesson 5: Multiplication All partials multiplication method Commutative property Compact multiplication method Partial product Making Money URG pg N.6, 5.N., 5.N6, 5.N.7, 5.A.7 Estimating products. Using convenient numbers for estimating. Multiplying numbers with ending zeros. Unit : Big Numbers Lesson 6: Estimating Products Convenient number Estimate DPP Item V Multiplication Practice 5.M. Developing number sense for large numbers. Collecting and using data to solve problems. Solving extended-response problems and communicating solution strategies Measuring length in centimeters Reading scientific notation Solving problems involving multiplication and division. Using the Solving and Telling Rubrics to selfassess problem-solving skills. Unit : Big Numbers Lesson 9: Stack Up Stack Up URG pg Student Rubric: Solving Student Rubric: Telling TIMS multidimensional Rubric 5.N., 5.N, 5.N6, 5.N., 5.N7 Various Supplemental Lessons and Sheets Provided DPP Item CC Quiz: 5 s and 0 s 5.N., 5.N., 5.N.3, 5.N., 5.N. Representing fractions using manipulatives and symbols Finding a fraction for a given quantity when unit whole is given Unit 3: and Lesson : Wholes and Parts Denominator Numerator DPP Item B Multiplication and Division Facts: s and 3 s Page of 7 Rondout Valley Central School District Last Updated August 3, 005

3 5.N.3, 5.N., 5.N.9, 5.N. 0, 5.N. Writing number sentences using fractions Representing fractions greater than one with pattern blocks Writing improper fractions as mixed numbers Writing mixed numbers as improper fractions Unit 3: and Lesson : Fraction Sentences Improper Fraction Mixed Number Proper Fraction 5.N.5, 5.N.5, 5.N.9, 5.N., A.7 Representing fractions using pattern blocks and number lines. Finding equivalent fractions. Unit : Exploring Numbers Lesson 3: Fraction Sentences Equivalent 5.N.5, 5.N.9, 5.N.0 Comparing and ordering fractions using benchmarks. Comparing and ordering fractions with common denominators. Comparing and ordering fractions with common numerators. Unit 3: and Lesson : Comparing Benchmarks Home Practice Part 6 A Fraction More 5.M.5, 5.N.6, 5.N.7, 5.S., 5.S. Using words, tables, graphs, and fractions to express ratios Finding equal ratios Using ratios to solve problems Unit 3: and Lesson 5: Using Ratio Quiz Time URG pg S.5, 5.S.7, 5.A., S., 5.S., 5.S.5, 5.S.5, 5.S.7 Sampling a population Averaging: finding the median. Making and interpreting bar graphs Predicting population characteristics from samples Collecting, organizing, graphing, and analyzing data ** Unit : Populations and Samples Lesson 5: Searching the Forest Collection folder Median Population Probability Rubric Sample Value Variable DPP Item K Subtraction Review DPP Item O Subtraction Review Page 3 of 7 Rondout Valley Central School District Last Updated August 3, 005

4 5.M., 5.M.5, 5.M7. 5.M.9, 5.M.0, 5.A.7, 5.S., 5.S., 5.N.6, 5.N.7 Using numerical variables Measuring length in yards and feet Averaging: finding the median Drawing and interpreting best fit lines Collecting, organizing, graphing, and analyzing data Using ratios to solve problems Using patterns in data to solve problems Translating between graphs and real-world events Unit 3: and Lesson 6: Distance Vs. Time Best fit line fixed variable speed DPP Item U Quiz: s and 3 s DPP Item V Goldfish on Sale Student Rubric: Knowing Student Rubric: Telling TIMS Multidimensional Rubric 5.N.6, 5.N.7 Solving multistep word problems Communicating solutions orally and in writing Choosing appropriate methods and tools to calculate (calculator, pencil and paper, or mental math) Choosing to find an estimate or an exact answer Unit 3: and Lesson 7: Speedy Problems 5.M., 5.M.5 Using strategies to the area of geometric figures. Using multiplication facts to find the area of geometric figures. Counting square centimeters to estimate the area of figures with curved sides Generalizing the area of a rectangle as length times width Unit : Division and Data Lesson : Grid Area Area Length Square Centimeter Width DPP Item B Multiplication and Division Facts: Square numbers DPP Item D Area of Shapes Finding Area 5.M., 5.M., 5.M.3, 5.M., 5.M.5, 5.M. Supplementary Work Provided Page of 7 Rondout Valley Central School District Last Updated August 3, 005

5 5.A.7, 5.N.3, 5.N.7 Modeling division with base-ten pieces. Dividing numbers ending with zeros Estimating quotients Interpreting remainders Unit : and Lesson : Modeling Division Dividend Divisor Quotient Remainder DPP Item F Counting Square Units 5.N.7, 5.N.8, 5.A. Supplement with Single Digit Division Practice Provided 5.S.3, 5.N.8 Reviewing the concept of mean. Comparing the mean and the median Averaging: finding the median and mean Using parentheses in numerical expressions. Using correct order of operations. Unit : and Lesson 5: Mean or Median? *(Order of Operations Post March) Average Mean Numerical Expression DPP Item Y medians and Means DPP Item Z Order of Operations 5.A.7, 5.S., 5.S., 5.N.6, 5.N. Measuring the area of irregular shapes. Collecting, organizing, graphing, and analyzing data. Using patterns in data to make predictions and solve problems. Drawing and interpreting best-fit lines Choosing an appropriate graph to display data Using ratios to solve problems Averaging: finding the median and mean. Using numerical variables Identifying the manipulated, responding, and fixed variables in an experiment Connecting mathematics and science to realworld situations Communicating solutions orally and in writing Unit : and Lesson 6: Spreading Out *Omit Explore pg. 36 Area Best-fit line Fixed variables Manipulated variable Responding variable DPP Item V DPP Item AA Quiz: Square numbers Page 5 of 7 Rondout Valley Central School District Last Updated August 3, 005

6 5.M.7, 5.N., 5.N5, 5.N.8 Finding a fraction for a given quantity when a unit whole is given Representing fractions and mixed numbers using geoboards, pictures, and symbols Unit 5: Investigating Lesson : Geoboard Denominator Fraction Numerator DPP Item B Multiplication and Division Facts: 9 s 5.N., 5.N.5, 5.N.0, 5.N. Representing fractions with pictures and symbols. Finding equivalent fractions. Writing addition and multiplication sentences with fractions Unit 5: Investigating Lesson 3: Using Dot Paper Rectangles Equivalent fractions 5.N., 5.N.5, 5.N.9 Comparing fractions using pictures and symbols. Finding common denominators. Unit 5: Investigating Lesson : Using Common Denominators Common Denominator Denominator Numerator 5.N., 5.N., 5.N. Grouping and counting by ones, tens, and hundreds. Representing two-and three-digit numbers using connecting cubes, base-ten pieces, place value charts, and symbols. Supplemental Work Provided (R05, R06, R07, 8-) Base-ten pieces Bit Flat Place value Skinny 5.M.0, 5.N., 5.N.5, 5.N.9, 5.N.0, 5.N., 5.N.5 Estimating differences of fractions using bench-marks such as 0, ½, and. Subtracting fractions with unlike denominators using pictures. Finding a common denominator for two or more fractions. Adding and subtracting fractions with unlike symbols Unit 5: Investigating *Optional Enrichment Lesson Lesson 7: Adding and Subtracting with Rectangles Common denominator Fraction Followup URG pg Page 6 of 7 Rondout Valley Central School District Last Updated August 3, 005

7 5.S. Using ratios to solve problems. Communicating solutions orally and in writing Translating between graphs and real-world events Unit 5: Investigating Lesson 8: Shannon s Trip to School 5.G.5, M.6, 5.M.8, 5.M. Estimating angle measures using benchmarks Measuring angles with a protractor Drawing angles of determined degrees Identifying acute, obtuse, and right angles Unit 6 Geometry Lesson : Angle Measures Acute Angle Angle Degree End point Obtuse angle Protractor Ray Right Angle Sides Straight Angle Vertex DPP Item B Multiplication and Division Facts: The Last Six Facts 5.G., 5.G.7, 5.G.8, 5.M.6, 5.M.8 Measuring angles Investigating properties of regular polygons Demonstrating that the sum of the angles in a triangle is 80 Identifying acute, right, and obtuse angles Unit 6 Geometry Lesson : Angles in Triangles and Other Polygons Polygon Quadrilateral Regular Polygon Trapezoid DPP Item M What s your Angle? Page 7 of 7 Rondout Valley Central School District Last Updated August 3, 005

8 5.G.5, 5.G.7, 5.M.6, 5.M.8, 5.A., 5.A., 5.S., 5.N.5 Investigating, describing, and reasoning about the results of subdividing polygons. Finding patterns in the sum of angles of polygons Investigating properties of regular polygons Making and testing conjectures about geometric properties Using numerical variables Expressing mathematical relationships using formulas Unit 6 Geometry Lesson 3: Polygon Angles Decagon Diagonal Dodecagon Equilateral Triangle Hexagon N-gon Nonagon Octagon Pentagon Regular Polygon Septagon Triangulating Journal Prompt 5.G., 5.G.9, 5.G.0, 5.M.5, 5.M.8, 5.N.5 Investigating properties of triangles Exploring congruence and similarity Making and testing conjectures about geometric properties Unit 6 Geometry Lesson : Congruent Shapes Congruent Similar DPP Item L Drawing Shapes 5.G.3 Describing and classifying two-dimensional shapes. Using mathematical Definitions Connecting Mathematics and Science: Classifying Animals Unit 6 Geometry Lesson 6: Classifying Shapes Convex Mammal Obtuse triangle Parallelogram Pentagon Polygon Quadrilateral Rectangle Rhombus Square Vertebrate Page 8 of 7 Rondout Valley Central School District Last Updated August 3, 005

9 5.G.7, 5.G.8, 5.M.3, 5.M.7, 5.M.8 Constructing polygons with specific measurements Constructing shapes with specific properties Using geometric concepts and skills to solve problems Communicating solutions orally and in writing Unit 6 Geometry Lesson 7: Making Shapes DPP Item Q Quiz: The Last Six Facts Student Rubric: Telling Slab Orders URG pg. 97 TIMS Multidimensional Rubric 5.G.9, 5.G.0, 5.G. Zeroing the two-pan balance. Comparing an ordering the mass of objects using a two-pan balance. Exploring the idea that mass depends on the material as well as the size of an object. Supplemental Lessons Symmetry R8, 0,67,79 Two-pan balance Mass 5.N.8, 5.N. Translating between different representations of decimals. (concrete, pictorial, symbolic) Using fractions, decimals, and percents to represent the same quantity Unit 7: Decimals and Probability Lesson :, Decimals, and Percents Centiwheel Decimal Fraction Percent Home Practice Part 3 Decimals and Percents 5.N.8, 5.N.9, 5.N.0, 5.N., 5.N. Translating between different representations of decimals (pictorial, symbolic) Understanding place value Reading and writing decimals to the thousandths Developing number sense for decimals Comparing and ordering decimals Unit 7: Decimals and Probability Lesson : Decimal Models Hundredths Ten-thousandths Tenths Thousandths Page 9 of 7 Rondout Valley Central School District Last Updated August 3, 005

10 5.M.7, 5.N.0, 5.N.8, 5.N. Comparing and ordering decimals Rounding decimals Unit 7: Decimals and Probability Lesson 3: Comparing and Rounding Decimals Bench marks Home Practice Part 5 Reading, Writing, and Ordering Decimals 5.N.8, 5.N.8, 5.N.3, 5.N.6 Adding and subtracting decimals using diagrams Adding and subtracting decimals using paper and pencil mehod Unit 7: Decimals and Probability Lesson : Adding and Subtracting Decimals DPP Item L Using the Centiwheel 5.N.8, 5.N.3, 5.N.6 Multiplying decimals using an area model Unit 7: Decimals and Probability Lesson 5: Multiplying Decimals with Area 5.N.7, 5.N.8, 5.N.0, 5.N., 5.N.6, 5.N.7 5.N.3, 5.N.6 Solving addition problems using calculators Estimating sums using benchmark numbers Using estimation to determine the reasonableness of results Supplemental Practice 96/97 Decimal Quiz URG pg. 9 MID TERM ASSESSMENT NEEDED Unit 8 Midyear Test (with Modifications) Page 0 of 7 Rondout Valley Central School District Last Updated August 3, 005

11 3 Interpreting as Division Finding Decimal equivalents (or decimal approximations) for fractions using the small centiwheel. Finding Decimal equivalents (or decimal approximations) for fractions using calculators. Identifying repeating decimals Unit 9: Connections to Division Lesson : and Division Repeating Decimals 3 5.N.6 Introducing lattice multiplication Multiplying digits X 3 digits using paper and pencil methods Comparing multiplication methods Unit 9: Connections to Division Lesson 3: Multiplication Methods Lattice Multiplication 3 5.N.7, 5.N.9, 5.N.0 Interpreting remainders in division problems Writing quotients as mixed numbers Solving division problems Unit 9: Connections to Division Lesson : Understanding Remainders DPP Item N - Operations Tie Dye Shirts URG pg N., 5.N., 5.N., 5.N.5, 5.N.6 Finding all the factors of numbers Identifying prime and composite numbers Unit : Number Patterns and Primes Lesson : Factor 0 Composite Factor Prime 3 5.N., 5.N. Identifying prime numbers Identifying and describing number patterns Unit : Number Patterns and Primes Lesson : Sifting For Primes Conjecture Cryptography Eratosthenes Sieve Twin Primes Page of 7 Rondout Valley Central School District Last Updated August 3, 005

12 3 5.N. Finding the prime factorization of a number Using exponents Unit : Number Patterns and Primes Lesson : Multiplication of *(Factor Trees Only) Exponent Factor Tree Prime Factorization Home Practice Part 3 Using Exponents 3 5.N., 5.N.9, 5.N.3 Finding common denominators Comparing fractions using common denominators Unit : Ways of Subtracting Larger Numbers Lesson 5: Comparing Common Denominator DPP Item P Finding Factors 3 5.N.5, 5.N.9, 5.N.0, 5.N. Reducing fractions to lowest terms Finding common denominators Adding and subtracting fractions using common denonminators Expressing a quotient as a mixed number Unit : Number Patterns and Primes Lesson 6: Reducing Lowest Term Reducing as a fraction Skills Check-up pg N.3 Supplemental T-Chart Lessons Page of 7 Rondout Valley Central School District Last Updated August 3, 005

13 5.A., 5.S., 5.S., 5.M.9, 5.N.9 Collecting, organizing, graphing, and analyzing data Making and interpreting bar graphs. Connecting mathematics and science to realworld situations. Establishing social norms for cooperation and discourse. Promoting the following beliefs:. Problems can be solved by more than one method;. Different methods should yield solutions that agree; and 3. Mathematics can be relevant and enjoyable. Unit : Populations and Samples Lesson : Eyelets Categorical Variable Data Mode Numerical Value Values Variable DPP Item C Addition Review DPP Item E Addition Review St. Crispin URG pg. 36 Using numerical variables. Naming values of variables. Collecting, organizing, graphing, and analyzing data. Making and interpreting bar graphs Investigating the concept of averages Averaging: finding the median Unit : Populations and Samples Lesson : Representing Data Average Median Numerical variable Value Variable 5.M.0, 5.S., 5.S.3, 5.S. Translating between graphs and real world events. Averaging: finding the median. Identifying the mode. Unit : Populations and Samples Lesson 3: Analyzing Data Mean Median Mode 5.N.7 Solving multistep word problem Communicating solutions orally and in writing Choosing appropriate methods and tools (calculator, pencil and paper, or mental math) Choosing to find an estimate or an exact answer Unit : Populations and Samples Lesson 6: Practice Problems Page 3 of 7 Rondout Valley Central School District Last Updated August 3, 005

14 5.N.8, 5.S.8 Reviewing the concept of the mean Comparing the mean and the median Averaging: finding the mean and the median Using the parenthesis in numerical expressions Using correct order of operations **Unit : Division and Data Lesson 5:Mean or Median **Order of Operations More Lessons Needed Average Mean Numerical Expression DPP Item Y Medians and Means DPP Item Z Order of Operations 5.N.0, 5.S.5, 5.S.6, 5.S.7 Collecting and analyzing data from a random process. Understanding that random even are predictable over the long run Defining probability. Exploring situations that have outcomes that are not equally likely. Unit 7: Decimals and Probability Lesson 7: Flipping One Coin Certain Equally Likely Impossible Probability 5.M.9, 5.N.0, 5.N.6, 5.N., 5.N.3,5.S., 5.S.5, 5.S.6, 5.S.6, 5.S.7 Analyzing fair and unfair games. Computing probabilities for all possible outcomes when coins are flipped. Expressing probabilities as fractions, decimals, and percents Collecting, organizing, graphing, and analyzing data. Making and interpreting bar graphs. Using probability to predict. Comparing probabilities with real world data Unit 7: Decimals and Probability Lesson 8: Flipping Two Coins Fair game Probability 5.M.9, 5.N.0, 5.N.6, 5.N., 5.N.3,5.S., 5.S.5, 5.S.6, 5.S.6, 5.S.7 Computing probabilities Expressing probabilities as fractions and percents Using probability to predict Comparing probabilities with real world data Unit 7: Decimals and Probability Lesson 9: Families with Two Children Supplemental Unit A Page of 7 Rondout Valley Central School District Last Updated August 3, 005

15 5.G., 5.G.3 Using coordinates to locate objects, find locations on maps, or plot points on graphs. Unit 0: Maps and Coordinates Lesson Introducing Cartesian Coordinates Axes Cartesian coordinates Ordered pairs Origin Quadrant Reef Home Practice Part 3 Working With Coordinates 5.G. Using coordinates Using negative numbers Unit 0: Maps and Coordinates Lesson 3: Wherefore art thou, Romeo? 5.G, 5.G.3, 5.M.3, 5.M., 5.N.3 Finding coordinates of an object relative to the origin. Plotting points using ordered pairs in the four quadrants. Making a four-quadrant map. Using a four-quadrant map to find distances. Unit 0: Maps and Coordinates Lesson : Mr. Origin Mr. Origin Coordinates: Getting to the Point URG pg. 5 5.A.8, 5.G., 5.G.3 Using slides to move shapes about the coordinate system. Determining the image of a slide. Unit 0: Maps and Coordinates Lesson 6: These Boots are Made for Sliding Congruent Corresponding parts Image Parallel Slide 5.A.8, 5.G., 5.G.3 Using flips to move shapes about the coordinate system. Determining the image of a flip. Unit 0: Maps and Coordinates Lesson 7: These Boots are Made for Flipping Flip Line of reflection Moving Shapes Page 5 of 7 Rondout Valley Central School District Last Updated August 3, 005

16 5.A.8, 5.G., 5.G.3 Using tessellations to create art. Connecting mathematics and art. Unit 0: Maps and Coordinates Lesson 9: Escher Drawings Tessellations 5.A., 5.A. Finding the area of rectangles Finding the area of polygons Using the formula of the area of a rectangle : A = l x w Using variables in formulas Unit 5: Developing Formulas with Geometry Lesson : Finding Area- Rectangles Area Congruent Formula Length Width 5.N.8 Using exponents Using correct order of operations Solving problems using geometric concept and skills. Unit 5: Developing Formulas with Geometry Lesson : Rectangle Riddles DPP Item C Area Rectangles Quiz 5.A., 5.A., 5.G., 5.G.6 Finding the area of triangles Identifying the base and height of triangles. Developing a formula for the area for the area of a triangle Using area to find the area of triangles: A = ½ x b x h Using variables in formulas Unit 5: Developing Formulas with Geometry Lesson : More Triangles Acute Triangle Altitude Base Height (altitude) Obtuse triangle Perpendicular 5.A., 5.A., 5.A.6, 5.G. Finding the perimeter of various shapes. Developing a formula for the perimeter of a rectangle Using variables in formulas Unit 5: Developing Formulas with Geometry Lesson 5: Perimeter Perimeter Area and Perimeter URG pg Page 6 of 7 Rondout Valley Central School District Last Updated August 3, 005

17 5.A., 5.A.6, 5.G., 5.M.3, 5.M.6, 5.M. Using geometric skills and concepts to solve problems. Solving multistep word problems. Communicating solutions orally and in writing. Choosing appropriate methods and tools to calculate (calculators, paper and pencil, or mental math). Unit 5: Developing Formulas with Geometry Lesson 6: A Variety of problems Home practice Part 6 Building A Park Unit 6: Bringing it all Together: an Assessment Unit Lesson 6: End-of-the-year Test Unit 6 End of Year Test Page 7 of 7 Rondout Valley Central School District Last Updated August 3, 005

Number and Operation Standard #1. Divide multi- digit numbers; solve real- world and mathematical problems using arithmetic.

Number and Operation Standard #1 MN Math Standards Vertical Alignment for Grade 5 Demonstrate mastery of multiplication and division basic facts; multiply multi- digit numbers; solve real- world and mathematical